Review: Describing Variables

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.title[
# Review: Describing Variables
]
.subtitle[
## The Effect Book: Chapter 3
]

---

# Outline

Read: [Chapter 3- Describing Variables](https://theeffectbook.net/ch-DescribingVariables.html)

- Descriptions of Variables

- Types of Variables

- The Distribution

- Summarizing the Distribution

- Theoretical Distributions

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# This Class

- We'll be discussion how we *describe variables* and *describe relationships*

- With a bit of an R reminder

- This class is much more concerned with *How is the data utilized?*

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#  Today

- We'll start with ways of discussing how we can *describe variables*
- And then move on to ways of discussing how we can *describe relationships*
- Secretly, pretty much all statistical analysis is just about doing one of those two things
- *Causal* analysis is *purely* about *knowing exactly which variables and relationships to describe*

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# Variables

- A statistical variable is a recorded observation, repeated many times

- "Number of calories I ate for breakfast this morning" is one observation

- "The number of calories I ate each breakfast in the past week" is a variable with seven observations

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# The Distribution of a Variable

- Variables have *distributions*
- The distribution of a variable is simply the description of *how often each value of the variable comes up*
- So for example, the statement "10% of people are left-handed" is just a partial description of the distribution of the handedness variable. 
- If you observe a bunch of people and record what their dominant hand is, 10% of the time you'll write down "left-handed," 1% of the time you'll write down "ambidextrous," and 89% of the time you'll write down "right-handed." That's the full description of the distribution

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# Looking Straight at a Distribution

- The distribution of a variable contains *everything we know* about that variable from empirical observation
- Any description we make will be a *summary* of that distribution
- So we may as well look at it directly!

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# Distributions of Kinds of Variables

- There are two main kinds of variables for which the distributions look different: discrete and continuous
- Discrete variables take a finite set of values
--

- Examples: left-handed, right-handed, ambidextrous. Or "lives in Seattle" vs. "Doesn't" or "Number of kids"

--
- Continuous variables take any value (many many values)

- Examples: `income`, `height`, `KwH of electricity used each day`

--
- (Sometimes, "ordinal" discrete variables with many values are treated as continuous for simplicity)

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# Discrete Distributions

- To fully describe the distribution of a discrete variable, just give the proportion of time it takes each value.

- Give a table with the proportions (or counts), or show a graph with the proportions

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# Discrete Distributions

```r
handedness_data <- data.frame(hand = c(rep('Left', 9*452),rep('Ambidextrous',.5*452),rep('Right',90.5*452))) #create data
library(tidyverse)
handedness_data %>% # dataset
  pull(hand) %>%  # choose the variable 
  table() %>%
  prop.table() # creates table with proportions
```

```
## .
## Ambidextrous         Left        Right 
##        0.005        0.090        0.905
```

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# Discrete Distributions

```r
ggplot(handedness_data, aes(x = hand)) + 
  geom_bar(fill = 'white', color = 'black') + # These two lines are important
  stat_count(geom = "text", size = 5,
             aes(label = scales::percent(..count../nrow(handedness_data)), 
                 y = ..count.. + 1300)) +
  ggpubr::theme_pubr() + 
  labs(x = 'Handedness', y = 'Count') # The rest is just decoration
```

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# Discrete Distributions

![](data:image/png;base64,#Review_1_files/figure-html/unnamed-chunk-3-1.png)
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# Using Discrete Distributions

- What can we use a discrete distribution to say?
- X% of observations are in category A
- (X+Y)% of observations are in category (A or B)
- If it's "ordinal" (the values have an order), we can describe the median, max, min, etc.